Krylov subspace methods are well suited to approximate many matrix functions; see, e.g.,
[1]}, [2]} for illustrations. They also have been applied successfully to the
approximation of tensor functions and the solution of tensor systems of equations; see
[3]}, [4]}, [5]}, [6]}, [7]} and references therein. It is therefore natural to seek to
approximate the tensor functions mentioned in the previous section by Krylov subspace
methods. We first discuss the application of the global tensor Arnoldi process to the
approximation of multilayer centrality measures, and subsequently consider the tensor
block Arnoldi process.
